Biology 3410, 6 February 2009
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Problem set #2: selection (improved edition!)
1. Strength of selection for AdhF on ethanol-soaked fly food. Cavener and Clegg (Evolution 35, 1-10,
1981) used wild-caught Drosophila melanogaster to establish experimental populations of flies that were
grown either on standard fly food (cornmeal-molasses-agar) or on the same food supplemented with 10%
ethanol. For 50 generations they tracked allele frequencies at 10 different enzyme loci that were
polymorphic for alleles that could be assayed by starch-gel electrophoresis of the proteins. Adh (alcohol
dehydrogenase) showed by far the strongest and most consistent pattern, which is summarized in the
original figure from the paper (left) and in the figure from your textbook (right) (Freeman and Herron,
Evolutionary Analysis, 4th edn, page 185).
The original figure plots the frequency of the Slow allele on the vertical axis, but the textbook figure plots
the frequency of Fast (i.e., it inverts the figure). Cavener and Clegg initiated all four experimental
populations with flies taken from the same laboratory stock population, so they did not directly control the
initial allele frequencies at any locus. Instead, the initial frequencies were those that occurred in the
laboratory stock that was used to initiate the experiment. The initial frequency of AdhF was p ≈ 0.35, so
the frequency of AdhS was q ≈ 0.65. (Note that the decimal points are missing from all but one of the
numbers on the vertical axis of Cavener and Clegg’s original figure.) The paper’s main conclusion is that
Fast was strongly favored in the ethanol-soaked experimental populations: by generation 50 it had fixed in
one and reached a frequency of almost 0.9 in the other. This was not particularly surprising, because FF
homozygotes were already known to show twice as much Adh enzyme activity as SS homozygotes.
From the data as displayed in the graphs you can estimate the relative fitnesses of the two alleles (Fast and
Slow) in the high-ethanol environments by fitting a simple model of selection to the observed (average)
change in allele frequencies over a given number of generations. To make things simple, let the fitness of
the SS homozygotes be 1-s relative to a fitness of 1 for the FF homozygotes, and assume that the fitness of
FS heterozygotes is intermediate (WFS = 1-½s, which is to say that the Fast and Slow alleles interact
additively, or are codominant, with respect to fitness). Your job is to estimate s, which is the relative
fitness difference between FF and SS homozygotes.
The expected change in allele frequency (from one generation to the
next) is a function of the marginal allelic fitnesses, the mean fitness,
and the allele frequency itself. Since these quantities all change with
the allele frequency, we can’t easily calculate Δp exactly for more than one generation at a time. But we
can approximate the multi-generational allele-frequency change under certain circumstances. For
example, with additive allelic interactions (heterozygote fitness intermediate between the homozygotes),
the difference between the two homozygote marginal fitnesses depends on s but not p, so it does not
change with the allele frequencies. And when the allele frequencies are not too far from 0.5, the product
pq remains close to 0.25. In addition, the mean fitness will always be fairly close to 1 unless s is very
large, so the denominator can simply be ignored. Thus, if we consider just the first few generations of the
experiment, when both alleles have frequencies near 0.5, we can approximate the one-generation change
in allele frequency as 0.25*(difference between the marginal fitnesses).
So, here’s a way to estimate s approximately. First, derive an algebraic expression for the difference
between the marginal fitnesses of the two alleles when the heterozygote fitness is intermediate. (It’s a
simple function of s only.) Second, from the graphs above, estimate the allele-frequency change in the
first few generations of the high-ethanol treatments, when both alleles have frequencies near 0.5.
(Obviously, you should average over the two replicates of this treatment. For example, after 5 generations
I would say that the average frequency of Fast has risen to around 0.5. You may think the best estimate is
a bit higher or lower than this, or you may prefer to use a different number of generations, like 10 or 15 or
20. That’s fine.) Third, turn your estimate of the total allele-frequency change into a per-generation
change (i.e., divide it by the number of generations from the beginning of the experiment). Finally, set
your expression for the one-generation change in allele frequency equal to your estimate of the average
allele-frequency change in the early generations of the experiment, and solve for s. WSS = 1-s.
2. Flower color, pollinators and dominance. White flowers (genotype rr) are recessive to red (RR and
Rr) in an outbreeding plant species. In a large random sample, you count 200 white-flowered plants and
800 red-flowered plants. What’s the frequency of the red allele (R)? One generation later, you count 250
white and 750 red plants. What was the change in allele frequency (of r and/or R)? If this change was
caused by a preference of the local pollinators (night-flying moths) for white flowers, and not by drift, or
selection at some linked locus, or magic or whatever, then what were the relative fitnesses of whiteflowered and red-flowered plants in the first (parental) generation?
Hint: There are harder and easier ways to frame this problem. It will make your life easier if you set the
fitness of red-flowered plants to 1.0, and focus on the frequency of the dominant R allele, which will then
have a marginal fitness of 1.0 regardless of its frequency.
3. Heterozygote advantage and homozygote lethality. Freeman and Herron use a computer simulation
to estimate the relative fitnesses of the three genotypes in the Mukai and Burdick experiment (VV, VL and
LL) as {0.74 : 1 : 0}. Derive this result “by hand”, using a simple extension of our general algebraic
model of selection (as explained in the lecture slides for February 4th, and on the natural selection
handout). Hint: At the interior allele-frequency equilibrium, p’ = p. This implies that [WV/W] = 1.
4. Harmful alleles at mutation-selection balance. Work out the expected allele and genotype
frequencies for deleterious recessive alleles with selection coefficients against the recessive homozygotes
of s = 0.01, 0.1 and 1, and with mutation rates (from the dominant “wild-type” allele to recessive
deleterious alleles) of 10-5, 10-6 and 10-7 per gene per generation (i.e., nine cases in all). What are the
implications for outbreeding species, on the assumption that many genetic loci have only minor “fine
tuning” functions, as suggested by the experiment of Thatcher, Shaw and Dickinson?